Journal of Economic Methodology ISSN 1350-178X print/ISSN 1469-9427 online © 2000 Taylor & Francis Ltd

http://www/tandf.co.uk/journals

Journal of Economic Methodology 7:2, 195–210 2000

Three attitudes towards data mining

Kevin D. Hoover and Stephen J. Perez

Abstract

‘Data mining’ refers to a broad class of activities that have in common,

a search over different ways to process or package data statistically or econo-

metrically with the purpose of making the final presentation meet certain design

criteria. We characterize three attitudes toward data mining: first, that it is to

be avoided and, if it is engaged in, that statistical inferences must be adjusted to

account for it; second, that it is inevitable and that the only results of any interest

are those that transcend the variety of alternative data mined specifications ( a view

associated with Leamer’s extreme-bounds analysis); and third, that it is essential

and that the only hope we have of using econometrics to uncover true economic

relationships is to be found in the intelligent mining of data. The first approach

confuses considerations of sampling distribution and considerations of epistemic

warrant and, reaches an unnecessarily hostile attitude toward data mining. The

second approach relies on a notion of robustness that has little relationship to truth:

there is no good reason to expect a true specification to be robust alternative

specifications. Robustness is not, in general, a carrier of epistemic warrant. The

third approach is operationalized in the general-to-specific search methodology

of the LSE school of econometrics. Its success demonstrates that intelligent data

mining is an important element in empirical investigation in economics.

Keywords:

data mining, extreme-bounds analysis, specification search, general-

to-specific, LSE econometrics

1 INTRODUCTION

To practice data mining is to sin against the norms of econometrics, of

that there can be little doubt. That few have attempted to justify professional

abhorrence to data mining signifies nothing, few have felt any pressing need

to justify our abhorrence of theft either. What is for practical purposes beyond

doubt needs no special justification; and we learn that data mining is bad

econometric practice, just as we learn that theft is bad social practice, at

our mothers’ knees as it were. Econometric norms, like social norms, are

internalized in an environment in which explicit prohibitions, implicit

example and, many subtle pressures to conformity mold our morés. Models

of ‘good’ econometric practice, stray remarks in textbooks or lectures, stern

warnings from supervisors and referees, all teach us that data-mining is

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abhorrent. All agree that theft is wrong, yet people steal and, they mine data.

So, from time to time moralists, political philosophers and legal scholars find

it necessary to raise the prohibition against theft out of its position as a back-

ground presupposition of social life, to scrutinize its ethical basis, to dis-

criminate among its varieties, to categorize various practices as falling inside

or outside the strictures that proscribe it. Similarly, the practice of data mining

has itself been scrutinized only infrequently (e.g., Leamer 1978; 1983, Mayer

1980, 1993; Lovell 1983; Hoover 1995). In this paper, we wish to characterize

the practice of data mining and three attitudes towards it. The first attitude is

the one that that we believe is the most common in the profession namely, data

mining is to be avoided and, if it is engaged in, we must adjust our statistical

inferences to account for it. The second attitude is that data mining is

inevitable and that the only results of any interest are those that transcend the

variety of alternative data mined specifications. The third attitude is that data

mining is essential and that the only hope that we have of using econometrics

to uncover true economic relationships is to be found in the intelligent mining

of data.

2 WHAT IS DATA MINING?

‘Data mining’ refers to a broad class of activities that have in common a search

over different ways to process or package data statistically or econometrically

with the purpose of making the final presentation meet certain design criteria.

An econometrician might try different combinations of regressors, different

sample periods, different functional forms, or different estimation methods

in order to find a regression that suited a theoretical preconception, had

‘significant’ coefficients, maximized goodness-of-fit, or some other criterion

or set of criteria. To clarify the issues, consider a particularly common sort

of data mining exercise. The object of the search is the process that generates

y

, where

y

= [y

t

], an N

´

1 vector of observations, t = 1, 2, ... N. Let

X

= {X

j

},

j = 1, 2, ... M, be the universe of variables over which a search might be

conducted. Let

X

P

=

XX

, the power set of

X

(i.e., the set of all subsets of

X

).

If

y

were generated from a linear process, then the actual set of variables that

generated it is an element of

X

P

. Call this set of true determinants

X

T

Î

X

P

,

and let the true data-generating process be:

y

k

=

X

k

T

b

T

+ v

k

,(1)

where

w

k

= [

w

k

t

], the vector of error terms, and k indicates the different

realizations of both errors and the variables in

X

. Now, let

X

i

Î

X

P

be any set

of variables; these define a model:

y

k

=

X

k

i

b

i

+ «

k

i

,(2)

where «

k

= [

e

k

t

] includes

w

k

, as well as every factor by which equation

(2) deviates from the true underlying process in equation (1). Typically, in

Three attitudes towards data mining 197

¯

economics only one realization of these variables is observed, k is degenerate

and takes only a single value. In other fields, for example in randomized

experiments in agriculture and elsewhere, k truly ranges over multiple realiz-

ations, each realization it is assumed, coming from the same underlying

distribution. While in general, regressors might be random (the possibility

indicated by the superscript k on

X

i

), many analytical conclusions require the

assumption that

X

i

remains fixed in repeated samples of the error term.

1

This

amounts to,

X

k

i

=

X

h

i

,

;

k, h, while,

e

k

¹

e

h

,

;

k

¹

h, except on a set of measure

zero.

We can estimate the model in equation (2) for a given i and any particular

realization of the errors (a given k). From such estimations we can obtain

various sample statistics. For concreteness, consider the estimated standard

errors that correspond to b

ˆ

i

the estimated coefficients of equation (2) for

specification i.

2

What we would like to have are the population standard errors

of the elements of b

ˆ

i

about b

ˆ

i

. Conceptually, they are the dispersion of the

sampling distribution of the estimated coefficients while

X

i

remains fixed

in repeated samples of the error term. Ideally, sample distributions would

be calculated over a range of k’s, and as k approached infinity, the sample

distributions would converge to the population distributions. In practice there

is a single realization of

e

k

. While conceptually this requires a further

assumption that the errors at different times are drawn from the same distri-

bution (the ergodic property), the correct counterfactual question remains:

what would the distribution be if it were possible to obtain multiple realiz-

ations with fixed regressors? Conceptually, the distribution of sample statistics

is derived from repeatedly resampling the residual within a constant specifi-

cation. This is clear in the case of standard errors estimated in Monte Carlo

settings or from bootstrap procedures.

3

In each case, simulations are pro-

grammed that exactly mimic the analysis just laid out.

Data-mining in this context amounts to searching over the various

X

i

Î

X

P

in order to meet selection criteria: e.g., that all of the t-statistics on the ele-

ments of

X

i

be statistically significant or that R

2

be maximized.

3 ONLY OUR PREJUDICES SURVIVE

Data mining is considered reprehensible largely because the world is full of

accidental correlations, so that what a search turns up is thought to be more

a reflection of what we want to find than what is true about the world. A

methodology that emphasizes choice among a wide array of variables based

on their correlations is bound to select variables that just happen to be related

in the particular data set to the dependent variables, even though there is no

economic basis for the relationship. One response to this problem is to ban

search altogether. Econometrics is regarded as hypothesis testing. Only a well

specified model should be estimated and if it fails to support the hypothesis, it

fails; and the economist should not search for a better specification.

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A common variant of this view, however, recognizes that search is likely

and might even be useful or fruitful. However, it questions the meaning of the

test statistics associated with the final reported model. The implicit argument

runs something like this: Conventional test statistics are based on independent

draws. The tests in a sequence of tests on the same data used to guide the

specification search are not necessarily independent. The test statistics for

any specification that has survived such a process are necessarily going to be

‘significant’. They are ‘Darwinian’ in the sense that only the fittest survive.

Since we know in advance that they pass the tests, the critical values for the

tests could not possibly be correct. The critical values for such Darwinian test

statistics must in fact be much higher. The hard part is to quantify the appro-

priate adjustment to the test statistics.

The interesting thing about this attitude towards data mining is the role that

it assigns to the statistics. In the presentation of the textbook interpretation

in the last section, those statistics were clearly reflections of sampling

distribution. Here the statistics are proposed as measures of epistemic

warrant, that is, as measures of our justification for believing a particular

specification to be the truth or as measures of the nearness of a particular

specification to the truth.

4

Sampling distribution is independent of the

investigator: it is a relationship between the particular specification and the

random errors thrown up by the world; the provenance of the specification

does not matter. Epistemic warrant is not independent of the investigator. To

take an extreme example, if we know an economist to be a prejudiced advocate

of a particular result and he presents us with a specification that confirms his

prejudice, our best guess is that the specification reflects the decision rule -

search until you find a confirming specification.

Not all search represents pure prejudice but, if test statistics are conceived

of as measures of epistemic warrant, the standard statistics will not be

appropriate in the presence of search. Michael Lovell (1983) provides an

example of this epistemic approach to test statistics. He argues that critical

values must be adjusted to reflect the degree of search. Lovell conducts a

number of simulations to make his point. In the first set of simulations, Lovell

(1983: 2

–

4) considers a regression like equation (2) in which the elements of

X

are mutually orthogonal. He considers sets of regressors that include exactly

two members (i.e., a fairly narrow subset of

X

P

). The dependent variable

y

is actually purely random and unrelated to any of the variables in

X

(i.e.,

X

T

=

Æ)

. Using five per cent critical values, he demonstrates that one or

more significant t-statistics occur more than five percent of the time. He pro-

poses a formula to correct the critical values to account for the amount of

search.

Lovell (1983: 4

–

11) also considers simulations in which there are genuine

underlying relationships and the data are not mutually orthogonal. He uses a

data set of twenty actual macroeconomic series as the universe of search

X

.

Subsets of

X

(i.e.,

X

T

for the particular simulation)

with at most two members

Three attitudes towards data mining 199

are used to generate a simulated dependent variable. He then evaluates the

success of different search algorithms in recovering the particular variables

used to generate the dependent variable. These algorithms are different methods

for choosing a ‘best’ set of regressors as

X

i

ranges over the elements of

X

P

?

Success can be judged by the ability of an algorithm to recover

X

T

. Lovell

also tracks the coefficients on individual variables X

g

Î

X

, noting whether or

not they are statistically significant at conventional levels. He is, therefore,

able to report empirical type I and type II error rates (i.e., size and power). As

in his first simulation, he finds that there are substantial size distortions, so that

conventional critical values would be grossly misleading. What is more, he

finds low empirical power, which is related to the algorithms inability to

recover

X

T

. The critical point for our purposes is that Lovell’s simulations

implicitly interpret test statistics as measures of epistemic warrant. The standard

critical value or the size of the test refers to the probability of a particular

t-statistic on repeated draws of

w

k

(k taking on multiple values) from the same

distribution (that is the significance of the textbook assumption that the

regressors are fixed in repeated samples). Lovell’s experiment, in contrast,

takes the error term in the true data-generating process,

w

k

, to be fixed (there

is a single k for each simulation) but, considers the way in which the distri-

bution of

e

k

i

, the estimated residual for each specification considered in the

search process, varies with every new

X

i

. Lovell’s numbers are correct but the

question they answer refers to a particular application of a particular search

procedure rather than to any property of the specification independently in

relation to the world.

The difficulty with interpreting test statistics in this manner is that the

actual numbers are specific for a particular search procedure in a particular

context. This is obvious if we think about how Lovell or anyone would con-

duct a Monte Carlo simulation to establish the modified critical values or sizes

of tests. A particular choice must be made for which variables appear in

X

and

a particular choice procedure must be adopted for searching over elements of

X

P

. Furthermore, one must establish a measure of the amount of search and

keep track of it. Yet, typically economists do not know how much search

produced any particular specification, nor is the universe of potential

regressors well defined. We do not start with a blank slate. Suppose, for

example, we estimate a ‘Goldfeld’ specification for money demand (Goldfeld

1973; also Judd and Scadding 1982). How many times has it been estimated

before? What do we know in advance of estimating it about how it is likely to

perform? What is the range of alternative specifications that have been or

might be considered? A specification such as the Goldfeld money demand

equation has involved literally incalculable amounts of search. Where would

we begin to assign epistemically relevant numbers to such a specification?

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4 ONLY THE ROBUST SHOULD SURVIVE

Edward Leamer (1978, 1983; and in Hendry et al. 1990) embraces the impli-

cation of this last question. He suggests immersing empirical investigation in

the vulgarities of data mining in order to exploit the ability of a researcher

to produce differing estimates of coefficient values through repeated search.

Only if it is not possible for a researcher to eliminate an empirical finding

should it be believed. Leamer is a Bayesian. Yet, Bayesian econometrics

present a number of technical hurdles that prevent even many of those who,

like Leamer, believe that it is the correct way to proceed in principle from

applying it in practice. Instead, Leamer suggests a practicable alternative to

Bayesian statistics: extreme bounds analysis. The Bayesian question is, how

much incremental information is there in a set of data with which we might

update our beliefs? Leamer (1983) and Leamer and Leonard (1983) argue

that, if econometric conclusions are sensitive to alternative specifications,

then they do not carry much information useful for updating our beliefs. Data

may be divided into free variables, which theory suggests should be in a

regression; focus variables, a subset of the free variables which are of

immediate interest; and doubtful variables, which competing theories suggest

might be important.

5

Leamer suggests estimating specifications that corre-

spond to every linear combination of doubtful variables in combination with

all of the free variables (including the focus variables). The extreme bounds of

the effects of the focus variables are given by the endpoints of the range of

values (

±

2 standard deviations) assigned to the coefficients on each of them

across these alternative regressions. If the extreme bounds are close together

then there can be some consensus on the import of the data for the problem at

hand; and if the extreme bounds are wide, that import is not pinned down very

precisely. If the extreme bounds bracket zero, then the direction of the effect is

not even clear. Such a variable can be regarded as not robust to alternative

specification.

6

The linkage between extreme bounds analysis and Bayesian principles

is not, however, one-to-one in the sense that the central idea, robustness to

alternative specification, represents an attitude to data-mining held by non-

Bayesians as well. Thomas Mayer’s (1993, 2000) argument that every

regression run by an investigator, not just the final preferred specification,

ought to be reported arises from a similar notion of robustness. If a coefficient

is little changed under a variety of specifications, we should have confidence

in it, and not otherwise. Mayer’s proposal that the evidence ought not to

be suppressed, but reported, at least in a summary fashion (e.g., as extreme

bounds) is, he argues, an issue of honest communication and not a deep episte-

mological problem. But we believe that this is incorrect. The epistemological

issue is this: if all the regressions are reported, just what is anyone supposed to

conclude from them?

The notion of robustness here is an odd one, as can be seen from a simple

Three attitudes towards data mining 201

example. Let A, B, and C be mutually orthogonal variables. Let a linear com-

bination of the three and a random error term determine a fourth variable D.

Now if the coefficient on C relative to its variance is small compared with the

coefficients on A and B relative to their variances and, the variance of C is

small relative to the variance of the error term, then the coefficient on C may

have a low conventionally calculated t-statistic and a high standard error. C

has a low signal-to-noise ratio. Let us suppose that C is just significant at a

conventional level of significance (say, five per cent) when the true specifi-

cation is estimated. How will C fare under extreme bounds analysis? The

omission of A, B or both, is likely to raise the standard error substantially

and the point estimate of the coefficient on C plus or minus twice its standard

deviation might now bracket zero.

7

We would then conclude that C is not

a robust variable and that it is not possible to reach a consensus, even though

ex hypothesi it is a true determinant of D.

One response might be that it is just an unfortunate fact that sometimes

the data are not sufficiently discriminating. The lack of robustness of variable

C tells us that, while there may be a truth, we just do not have enough

information to narrow the range of prior beliefs about that truth, despite the

willingness of investigators to consider the complete range of possibilities.

The difference between the real world and the example here is that, unlike here

we never know the actual truth. Thus, if we happen to estimate the truth, yet

the truth is not robust, our true estimate carries little conviction or epistemic

warrant.

A second response, however, is that the example here illustrates that there is

no good reason to expect a true specification to be robust

–

that is, to be robust

to mis-specification. Robustness is not, in general, a carrier of epistemic warrant.

Leamer (in Hendry et al. 1990: 188) attacks the very notion of a true specifi-

cation:

I ... don’t think there is a true data-generating process ...

To me the essential difference between the Bayesian and a classical point

of view is not that the parameters are treated as random variables, but

rather that the sampling distributions are treated as subjective distributions

or characterizations of states of mind ... And by ‘states of mind’ what I

mean is the opinion that it is useful for me to operate as if the data were

generated in a certain way.

Econometrics for Leamer is about characterizing the data but not about dis-

covering the actual processes that generated the data. We find this position to

be barely coherent. The relationships among data are interesting only when

they go beyond the particular factual context in which they are estimated.

If we estimate a relationship between prices and quantities, for instance, we

might wish to use it predictively (what is our best estimate of tomorrow’s

price?) or counterfactually (if the price had been different, how would the

quantity have been different?). Either way, the relationship is meant to go

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beyond the observed data and apply with some degree of generality to an

unobserved domain. To say that there is a true data-generating process is to

say that a specification could in principle, at least approximately, capture that

implied general relationship. To deny this would appear to defeat the purpose

of doing empirical economics. The very idea of a specification in which

different observations are connected by a common description seems to imply

generality. The idea of Bayesian updating of a prior with new information

seems to presuppose that the old and the new information refer to a common

relationship among the data

–

generality once more.

5 THE TRUTH IS SPECIALLY FITTED TO SURVIVE

The third attitude to data mining embraces the notion that there is a true data-

generating process, although recognizing that we cannot ever be sure that we

have uncovered it. A good specification-search methodology is one in which

the truth is likely to emerge as the search continues on more and more data. On

this view, data mining is not a term of abuse but a description of an essential

empirical activity. The only issue is whether any particular data mining

scheme is a good one. This pro-data mining attitude is most obvious in the so-

called LSE (London School of Economics) methodology.

8

The relevant LSE

methodology is the general-to-specific modelling approach. It relies on an

intuitively appealing idea. A sufficiently complicated model can, in principle,

describe the economic world.

9

Any more parsimonious model is an improve-

ment on such a complicated model if it conveys all of the same information in

a simpler, more compact form. Such a parsimonious model would necessarily

be superior to all other models that are restrictions of the completely general

model except, perhaps, to a class of models nested within the parsimonious

model itself. The art of model specification in the LSE framework is to seek

out models that are valid parsimonious restrictions of the completely general

model and, that are not redundant in the sense of having an even more parsi-

monious model nested within them that also are valid restrictions of the com-

pletely general model.

The general-to-specific modelling approach is related to the theory of

encompassing.

10

Roughly speaking, one model encompasses another if it con-

veys all of the information conveyed by another model. It is easy to understand

the fundamental idea by considering two non-nested models of the same

dependent variable. Which is better? Consider a more general model that uses

the non-redundant union of the regressors of the two models. If model I

is a valid restriction of the more general model (e.g., based on an F-test) and

model II is not, then model I encompasses model II. If model II is a valid

restriction and model I is not, then model II encompasses model I. In either

case, we know everything about the joint model from one of the restricted

models, we therefore know everything about the other restricted model from

that one. There is, of course, no necessity that either model will be a valid

Three attitudes towards data mining 203

restriction of the joint model: each could convey information that the other

failed to convey. A hierarchy of encompassing models arises naturally in a

general-to-specific modeling exercise. A model is tentatively admissible on

the LSE view if it is congruent with the data in the sense of being: (i) consistent

with the measuring system (e.g., not permitting negative fitted values in cases

in which the data are intrinsically positive); (ii) coherent with the data in that

its errors are innovations that are white noise as well as a martingale difference

sequence relative to the data considered; and (iii) stable (cf. Phillips 1988:

352

–

53; Mizon 1995: 115

–

22; White 1990: 370

–

74). Further conditions

(e.g., consistency with economic theory, weak exogeneity of the regressors

with respect to parameters of interest, orthogonality of decision variables)

may also be required for economic interpretability or, to support policy inter-

ventions or other particular purposes. If a researcher begins with a tentatively

admissible general model and pursues a chain of simplifications, at each

step maintaining admissibility and checking whether the simplified model is a

valid restriction of the more general model, then the simplified model will be a

more parsimonious representation of all the models higher on that particular

chain of simplification and will encompass all of the models lower along the

same chain.

The general-to-specific approach might be seen as an example of invidious

data mining. The encompassing relationships that arise so naturally apply only

to a specific path of simplifications. One objection to the general-to-specific

approach is that there is no automatic encompassing relationship between

the final models of different researchers, who have wandered down different

paths in the forest of models nested in the general model. One answer to this

is that any two models can be tested for encompassing either through the

application of non-nested hypothesis tests or through the approach described

above, of nesting them within a joint model. Thus, the question of which, if

either, encompasses the other can be resolved, except in cases in which sample

size is inadequate.

A second objection notes that variables may be correlated either because

there is a genuine relation between them or because

–

in short samples

–

they

are adventitiously correlated. This is the objection of Hess et al. (1998) that

the general-to-specific specification search of Baba et al. (1992) selects

an ‘overfitting’ model. Any search algorithm that retains significant variables

will be subject to this objection since adventitious correlations are frequently

encountered in small samples. They can be eliminated only through an appeal

to wider criteria, such as agreement with a priori theory. One is entitled to ask

though, before accepting this criticism, on what basis should these criteria be

privileged?

By far the most common reaction of critical commentators and referees to

the general-to-specific approach questions the meaning of the test statistics

associated with the final model. The idea of Darwinian test statistics arises, as

it does for Lovell, because test statistics which are well-defined only under the

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correct specification, are compared across competing (and, therefore, necessarily

not all correct) specifications.

The general-to-specific approach is straight-forward regarding this issue.

It accepts that choice among specifications is unavoidable, that an economic

interpretation requires correct specification and that correct specification

is not likely to be given a priori. The general-to-specific search treats and

focuses on the relationship between the specification and the data, rather than,

as is the case with the other two attitudes, on the relationship between the

investigator and the specification. That is, it interprets the test statistics as

evidence of sampling distribution rather than as measures of epistemic

warrant. Each specification is taken on probation. The question posed is

counterfactual: what would the sampling distributions be if the specification in

hand were in fact the truth? The true specification, for example, by virtue of

recapitulating the underlying data-generating process, should show errors

that are white noise innovations. Similarly, the true specification should

encompass any other specification (in particular it should encompass the higher

dimensional general specification in which it is nested).

The general-to-specific approach is Darwinian but in a different sense than

that implied in the other two attitudes. The notion that only our prejudices

survive, or that the key issue is to modify critical values to account for the

degree of search, assumes that we should track some aspect say, the coefficient

on a particular variable, through a series of mutations (the alternative specifi-

cations) and that the survival criterion is our particular prior commitment to

a value, sign or level of statistical significance for that variable. The general-

to-specific methodology rejects the idea that it makes sense to track an aspect

of an evolving specification. Since the specification is regarded as informative

about the data rather than about the investigator or the history of the investi-

gation, each specification must be evaluated independently. Nor should our

preconceptions serve as a survival index. Each specification is evaluated for

its verisimilitude (does it behave statistically like the truth would behave were

we to know the truth?) and, for its relative informativeness (does it encompass

alternative specifications?). The surviving specification in a search is a model

of the statistical properties of the data and identical specifications bear the

same relationship to the data whether that search was an arduous bit of data

mining or a directly intuited step to the final specification.

Should we expect the distillation process to lead to the truth? The Darwinian

nature of the general-to-specific search methodology can be explained with

reference to a remarkable theorem due to Halbert White (1990: 379

–

80). The

upshot of which is this: for a fixed set of specifications and a battery of specifi-

cation tests, as the sample size grows toward infinity and increasingly smaller

test sizes are employed, the test battery will

–

with a probability approaching

unity

–

select the correct specification from the set. In such cases, White’s

theorem implies that type I and type II error both fall asymptotically to zero.

White’s theorem says that, given enough data, only the true specification will

Three attitudes towards data mining 205

survive a stringent enough set of tests. This turns the criticisms which regard

data mining as Darwinian, in a pejorative sense, on their heads. The critics fear

that the survivor of sequential tests survives accidentally and, therefore, that

the critical values of such tests ought to be adjusted to reflect the likelihood

of an accident. White’s theorem suggests that the true specification survives

precisely because the true specification is necessarily, in the long run, the

fittest specification.

Approaches that focus on correcting critical values miss the point. White’s

theorem suggests that we envisage the problem differently. An analogy is the

fitting together of a jigsaw puzzle. Even if a piece duplicates another in part or

all of its shape, as more pieces are put into place, the requirement that the

surface picture as well as the geometry of the pieces cohere implies that each

piece has a unique position. Inferences about the puzzle as a whole, or

the piece in relation to the puzzle, can be made soundly only conditional on

getting the pieces into their proper positions. And, in the long run, the puzzle

fits together only one way

–

a fact about the puzzle itself, not about us.

White’s theorem is an asymptotic result. The real world of economics does

not deal in infinite samples of data. But the general-to-specific methodology

proceeds from a similar vision of the relationship of testing to the truth. The

interesting methodological question on this view is, what are effective pro-

cedures for solving the jigsaw puzzles of economics when samples are small?

We have made a first pass at this question.

Hoover and Perez (1999) evaluate the general-to-specific methodology in a

simulation study inspired by Lovell’s (1983) Monte Carlo study of mechan-

ized search algorithms (see section 3 above). Lovell concludes that the three

simple algorithms he examines (step-wise regression, maximum R

2

and max-

min t-statistics) are all quite poor in recovering the true data-generating

processes. Furthermore, the size and power of the algorithms taken as a whole

(that is the ability of the algorithms to exclude variables that were not in

the data-generating process and to include variables that were) is rather poor

and quite different from that implied by conventional critical values based on

sampling distributions. Using updated data and the same data-generating pro-

cesses, we are able to confirm Lovell’s results for the algorithms he tests on

annual data.

We then extend the investigation to the general-to-specific search proce-

dure. We use the same variables but at a quarterly frequency and we difference

each series until it is stationary on standard tests. In the hands of econo-

metricians of the LSE school, the general-to-specific methodology is not

mechanical like Lovell’s step-wise regression or other algorithms. Neverthe-

less, we have developed a mechanical algorithm that mimics some key features

of the general-to-specific approach. It begins with a general model in which

the entire set of variables in Lovell’s data set (included lagged variables) appears

as regressors. This regression is tested for congruence. If it passes, simplifi-

cation begins. Regressors with the low t-statistics are deleted in sequence,

206 Articles

starting a different search with each of the ten lowest, providing that they

are insignificant at conventional sizes. When a regressor is deleted and a new

estimate obtained, it is checked to see whether it encompasses the general

model. If it does not or if it fails any tests of congruence, the regressor is

replaced and the variable with the next lowest t-statistic from the previous

regression is eliminated instead. If it does, then the variable with the next lowest

insignificant t-statistic in the current regression is eliminated and, the process

of testing is repeated. Elimination continues until either all retained variables

are significant, no variables can be removed without failing congruence, or no

variables can be removed without failing to encompass the general model. Ten

such regressions from ten search paths, corresponding to the ten regressors

with lowest t-statistics in the general model, constitute the possible character-

izations of the data. The model among these ten that encompasses the others is

chosen as the final model.

11

Lovell, and proponents of the first view of data-mining would have us

report this specification but, adjust the standard errors of the coefficients to

account for the many regressions run. Leamer and proponents of the second

view of data mining would have us look at all of the many regressions and

choose only those variables that do not have their coefficient values change

significantly over the search, i.e. the end result is not important, only the distri-

bution of the coefficients estimates is important. The general-to-specific approach

takes the final specification to represent the best approximation to the truth

because it acts as closely to how the truth would act, if we knew it. Evolution is

important but not the history of evolution.

To check the success of this algorithm, we simulate with the updated quarterly

data the same models that Lovell uses. There are nine models, static and

dynamic, calibrated from the actual data. The independent variables are actual

data but the dependent variable is simulated from the actual independent

variables and draws from a random distribution with characteristics that match

the performance of each model in actual data. We conduct 1000 simulations

and searches of each model. In contrast to Lovell’s algorithms, we find that

the general-to-specific methodology is effective at recovering the true data-

generating process. It does not always succeed. Where it fails, it seems to be

almost exclusively because of low signal-to-noise ratios. This is reflected in

the fact that both size and power measures are close to what one obtains from

Monte Carlo simulations in which the true specification is known in advance.

It also shows that no method could be expected in some cases to find the true

model when there is simply not enough information in the data. Our results are

supportive of the general-to-specific methodology but they are limited. Work-

in-progress aims to extend the evaluation to non-stationary data, in which

questions of cointegration are important, and to cross-sectional contexts.

The point of this long digression is not principally to advertise our own

work although we are happy if it does that. Rather it is to demonstrate an

empirical spirit. We hope to have provided a theoretical analysis of why the

Three attitudes towards data mining 207

concerns of the opponents of data mining are misplaced but we also wish

to allay any nagging doubts by pointing to evidence that, practically, the

difficulties they foresee do not in fact arise.

6 CONCLUSION

Econometrics is a tool for learning about the economy. It presupposes the

existence of an economy to learn about and not an assortment of facts but, an

economy with real general features that imply the behaviour of the data and

constrain the way that econometric and statistical calculations package the

data. There is a truth about the economy that remains the truth, even though it

presents a different aspect when viewed through different econometric filters,

just as there is a truth about the moon or the crab nebula that remains the truth

even though these heavenly bodies appear differently when viewed through

different telescopes and optical filters. The central issue is how to use these

observations most effectively. The school of thought that argues that the more

the search, the lower the epistemic warrant would reject a detailed picture

of a distant galaxy because it was difficult to obtain. It concentrates on the

astronomer, rather than on the astronomical object. The problem is that

the object may be objectively difficult to find and may yield only to highly

structured search. Indeed, many scientific results are valued precisely because

they are difficult to obtain. The school of thought that seeks robustness rather

than truth would reject the picture because many other pictures of the same

sector of the sky processed in different ways look quite different. Whereas the

school of thought that we endorse argues that the issues that need to be

addressed are, first, whether the lenses and filters of the astronomers or the

statistics of the econometricians are in fact the ones that would reveal the

aspect of the truth that interests us

–

if it were there

–

and, second, whether, in

the event, they do so. A regulated specification search, such as the general-to-

specific methodology proposes, is an attempt to use econometrics to bring an

economic reality into focus that would otherwise remain hidden. It aims, quite

literally, to discover the truth.

Kevin D. Hoover

Department of Economics, University of California, USA

kdhoover@ucdavis.edu

Stephen J. Perez

Department of Economics, Washington State University, USA

sjperez@wsu.edu

ACKNOWLEDGEMENTS

The authors wish to thank Roger Backhouse, Peter Burridge, Alistair Hall,

Thomas Mayer, Mary Morgan and Steven Sheffrin for comments on earlier

drafts.

208 Articles

NOTES

1 This is not to deny that analytical conclusions are drawn with respect to models

with stochastic regressors. But even such models are characterized at some

level by probability distributions with constant parameters (cf. the debate

between Leamer and Hendry in Hendry et al. (1990: 195).

2 To keep the discussion simple, we will often speak of the standard errors and

t-statistics of regression coefficients as exemplars of the sampling distribution.

Our points are also relevant mutatis mutandis to other statistics.

3 On Monte Carlo methods, see Hendry (1995, ch. 3, section 6); on bootstrap

methods, see Jeong and Maddala (1993).

4 Sampling distribution and epistemic warrant are two distinct things. In particular,

epistemic warrant refers to the circumstances in which we have adequate justi-

fication for a belief. It is not the perfection of the sampling distribution in the

sense of being the population distribution that corresponds to the sample.

5 These categories are drawn from McAleer et al. (1985) and their restatement of

Leamer’s extreme bounds analysis.

6 It is important not to confuse the idea of robustness here with notions of temporal

stability or homogeneity among subsamples. Truth need not be constant over time

nor global for a given set of data. Robustness to alternative specification holds the

sample constant, so these questions do not arise; it is only the specification that

varies.

7 The point estimate itself will not switch signs if the regressors are orthogonal as

supposed but, might do so if they are correlated with each other.

8 The LSE approach is described sympathetically in Gilbert (1986), Hendry (1987,

1995, especially ch. 9–15), Pagan (1987), Phillips (1988), Ericsson et al. (1990)

and Mizon (1995). For more sceptical accounts, see Faust and Whiteman (1995)

and Hansen (1996). The adjective ‘LSE’ is, to some extent, a misnomer. It derives

from the fact that there is a tradition of time-series econometrics that began in the

1960s at the London School of Economics, see Mizon (1995) for a brief history.

The practitioners of LSE econometrics are now widely dispersed among aca-

demic institutions throughout Britain and the world.

9 This is a truism. Practically, however, it involves a leap of faith; for models that

are one-to-one, or even distantly approach one-to-one, with the world are not

tractable.

10 For general discussions of encompassing, see, for example, Mizon (1984), Mizon

and Richard (1986), Hendry and Richard (1987), Hendry (1988, 1995 ch. 14).

11 In this paper we use the necessary condition for encompassing that the standard

error of regression for the encompassing model must be the lowest of the ten. In

work in progress we conduct a sequence of encompassing tests to choose among

the ten, allowing for the fact that some linear combination of them might in fact

encompass the others, even while none of them does so individually.

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